On the basic equation of dynamics of a thread of variable length
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Abstract
Determination of the largest dynamic forces in hoisting ropes is associated with the study of oscillatory processes in a variable length thread with a load at the end. Differential equations of longitudinal vibrations of an elastic weighted thread were first derived and solved by N. P. Neronov. These equations and their exact solution obtained by the method of characteristics are complicated and inconvenient for practical application. However, brought to a numerical example, they can be used to compare approximate methods with the exact solution of the problem .
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References
- Zhuravlev P. A. To the dynamics of mine hoisting. In the collection: Steel Ropes, No. 2, Technics, 1965.
- Neronov N. P. About elastic deformations in a hoisting rope. Applied Mathematics and Mechanics, vol. 1, iss. 1, 1937.
- Neronov N. P. Determination of Tension in a Mine Hoisting Rope for a Load Suspension Point. Journal of Mining Institute, vol. XXXIX, iss. 3, 1961.